Renting car in Europe - uk_in_usa
I've not been back for years but will be coming over in May.

I was thinking of renting a car in Paris and driving it to Berlin and taking in a few of the Cold War sites like Marienborn/Helmstedt on the way

With the EU etc., is it now a no-brainer to rent a car in one European country and drive it to another ?

Renting car in Europe - Armitage Shanks {p}
No, it is possible but it is very expensive Effectively you have to pay the firm you hire from the cost ofreturning the car to the pick-up point, in mostcases.

Just get a quote for a hypothetical rental, from say Hertz, for the itinerary you want and stand by to be amazed. It is easier within a country but a cross border rental/drop off is not cheap
Renting car in Europe - Kiwi Gary
If you are officially non-resident in EU, and you can stand Peugeots, then Peugeot Open Europe is worth a look if you are staying for 3 weeks or more. We have used them twice, once returning to Paris and once drop-off at Heathrow. Remote drop-off is a bit steep because the vehicle has to be returned to France and you have to pay for them to send a driver over and ferry the car back, but can be cheaper than say Hertz one-way hires because the short-term lease rate is so much less.
Renting car in Europe - Armitage Shanks {p}
Hypothetical 7 day rental with Hertz, pick in Paris drop off in Berlin, is £500 for a Panda to £600 for a Laguna - high but not outrageous IMO
Renting car in Europe - Bagpuss
If you are talking about a one way rental, then you will have to pay additional fees to collect in one country and drop off in another, in the same way you do with one way interstate rentals in the US. Other than that there are no problems with insurance, etc provided you don't want to drive further east to the Czech Republic or somewhere in which case there will probably be surcharges.

If you drive to Germany with a French registered car, then you will probably find the German authorities will not be able to trace you for parking tickets, fines etc. This may make up for the fact that renting a car in France (in my experience) is more expensive than in Germany.

Beware when coming from the US that most rental cars have manual gearboxes, automatics cost more! You will also find that the diesel models which predominate in europe don't like being filled with petrol as an American colleague of mine can testify.
Renting car in Europe - uk_in_usa
I was actually planning to return it to France, i.e., not a 1-way rental. Should have made that clear.